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FRUITVITAON
Rozwiązane

Rozwiąż nierówność:
[tex]12x^{2} -36x+24\ \textless \ 0[/tex]

Odpowiedź :

CATTA1EYAON

[tex]12x^2-36x+24<0\\\Delta=(-36)^2-4*12+24\\\Delta=1296-1152=144\\\sqrt{\Delta}=\sqrt{144}=12\\x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12}{2*12}=\frac{36-12}{24}=\frac{24}{24}=1\\x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12}{2*12}=\frac{36+12}{24}=\frac{48}{24}=2\\[/tex]

[tex]a=12 | a>0 - \text{ramiona paraboli skierowane w gore}\\f(x)<0 \text{ dla } x \in (1; 2)[/tex]

BASETLAON

[tex]12x^{2}-36x+24 < 0 \ \ /:12\\\\x^{2}-3x+2 < 0\\\\\Delta = b^{2}-4ac = (-3)^{2}-4\cdot1\cdot2 = 9-8 = 1\\\\\sqrt{\Delta} = \sqrt{1} = 1\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}} = \frac{3-1}{2} = 1\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a} = \frac{3+1}{2} = 2\\\\a > 0, \ to \ ramiona \ paraboli \ skierowane do \ gory\\\\\boxed{x \in (1;2)}[/tex]

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